As a result of integrability a variety of steady and pulsating solution have been derived [1]}, [2]}. We will not recall the parametrization of three fundamental breathers on a finite-amplitude carrier as these have been discussed in many past publications [3]}, [4]}, [5]}, [6]}. The family of ABs describe the nonlinear stage of MI and are periodic in time when considering the framework (REF ), the PB is the limit case of zero modulation frequency, i.e. infinite modulation period, and the KBs the space periodic solution, which starts its evolution from a solitonic perturbation on the carrier. As such, the KB never converges to a uniform amplitude. All these solutions have been observed in a variety of nonlinear dispersive media and, for more details, we refer the reader to [3]}, [4]}, [9]}, [5]}, [6]}. In water waves the boundary conditions at beginning of the flume consist of time-series of surface displacement. The latter are driving the wave maker while its mechanical motion is linearly proportional to the surface elevation signal as determined by theory. To drive the wavemaker and to observe NLSE solitons or breathers, it is sufficient to use the expression of surface elevation defined to first-order of approximation [9]}
\(\eta (x,t)=\textnormal {Re}\left(\Psi \left(x,t\right)\exp \left[i\left(kx-\omega t\right)\right]\right).\) 
